Let's solve the given mathematical expression step by step:

$24 - |25 - 26 - \{(27 - 28 - 29)\}|$

First, we simplify the expression inside the braces $\{\cdot\}$:

$27 - 28 - 29$

Calculate the subtraction inside the braces:

$27 - 28 = -1$

Then:

$-1 - 29 = -30$

So, the expression inside the braces simplifies to $-30$:

$24 - |25 - 26 - (-30)|$

Next, we simplify the expression inside the absolute value $|\cdot|$:

$25 - 26 - (-30)$

Calculate the subtraction and addition inside the absolute value:

$25 - 26 = -1$

Then:

$-1 - (-30) = -1 + 30 = 29$

So, the expression inside the absolute value simplifies to $29$:

$24 - |29|$

Since the absolute value of 29 is 29, the expression becomes:

$24 - 29$

Finally, subtract 29 from 24:

$24 - 29 = -5$

So, the final result of the expression is:

$-5$

Would you like more details or have any questions about this solution? Here are some related questions you might want to ask:

1. How do you simplify expressions with nested parentheses?
2. What is the process for calculating absolute values?
3. Can you explain more about the order of operations in mathematics?
4. How do you handle negative numbers in subtraction?
5. What are some common mistakes to avoid when simplifying complex expressions?

Tip: When simplifying expressions with nested parentheses or absolute values, always start from the innermost expressions and work your way outwards.